Introduction. Results

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1 T h e H ig h -F re q u e n c y R o ta tio n a l S p e c tru m o f 1,1 -D ich lo ro eth y le n e Z. Kisiel and L. Pszczółkowski Institute of Physics, Polish Academy of Sciences, AI. Lotniköw 32/46, Warszawa, Poland Z. Naturforsch. 50a, (1995); received October 31, 1994 The b-type rotational spectrum of 1,1-dichloroethylene was investigated up to 450 GHz and was found to be dominated by type-ii R-type bands. All constants in the sextic Hamiltonian for the ground states of the common isotopic species and of the 37C1 isotopomer were determined from measurements on transitions with J up to 95. Quartic and sextic planarity defects were evaluated and are compared and discussed with those for several recently investigated planar molecules. Key words: mm-wave rotational spectroscopy, band spectra, sextic constants. Introduction With the increasing importance of atmospheric studies at millimeter and infrared wavelengths the accurate knowledge of rotational spectra well into the submillimeter region becomes mandatory. The rotational spectrum of the volatile solvent 1,1-dichloroethylene has previously only been studied at frequencies below 70 GHz [1] with measurements for the common species taken up to J = 45. The values of the nuclear quadrupole coupling constants and of the electric dipole moment are also known from the studies by Howe and Flygare [2, 3]. In the present work the coverage of the spectrum is extended by a factor of six in frequency and a factor of 2 in J through measurements with a BWO-based, source modulated spectrometer. Various tests are carried out to assess the reliability of the derived constants, and recent results for several molecules are collected to update the discussion of the higher order planarity defects to molecules higher than triatomic. Experimental details 1,1-dichloroethylene of >99% purity was purchased from Merck and was used without further purification. Measurements were made on a room-temperature sample contained in a 10 cm diameter, 3.5 m long absorption cell. The spectrometer and the data manipulation techniques have been described previously [4-6] and allow, through the use of high-frequency BWO sources in free-running mode, a broad- Reprint requests to Dr Z. Kisiel. banded, frequency agile coverage of frequencies up to ca. 500 GHz. Farran Technology SD-015 and SD-018 honeycomb Schottky diodes were used in the mixer for frequency measurement and in the detector, while for frequencies above 350 GHz a home-made superconducting InSb detector was preferred. Results The high frequency rotational spectrum of 1,1- dichloroethylene was found to be relatively sparse and dominated by type-ii R-type bands. These bands are formed from near-coincidence of transitions between rotational energy levels that are the first to become degenerate in the direction of the oblate symmetric top limit. Thus the first line in each band will be formed from transitions between the level pairs J 0 j, J a n d «J + li,j+i which are allowed by either na or fib dipole moment component. The succeeding line will be formed from transitions between j 11,j 2» j ~^2,j-2 and j 2,j-i levels, and for nb type transitions the quantum numbers of the two degenerate components of each line in the band will be given by k + ^k+l,j-2k+l*~j kkj-2k Ij ~ k + l fcj_2k+1< j kk + 1 j_2k where j is equal to J for the leading line in the band, and k = 0,1,2,3... The overlap of fia J + 10,j+i*~Jo,j and J + 1i,j+ i*-ji,j transitions was first noted by Borchert [7], who suggested the nomenclature 'type-ii' to distinguish from the common ar bands formed from overlaps of various K _ xtransitions for the same J +1 <- J. Extended type-ii bands were observed in the ^ / 95 / $ Verlag der Zeitschrift für Naturforschung, D Tübingen Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.v. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namensnennung 4.0 Lizenz. This work has been digitalized and published in 2013 by Verlag Zeitschrift für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License.

2 348 Z. Kisiel and L. Pszczölkowski Rotational Spectrum of 1,1-Dichloroethylene Fig. 1. The j 94 type-ii R-type band of the common isotopic species of 1,1-dichloroethylene overlapped with the j = 96 band of the 35C1 CI species. The constituent lines in these bands are each formed from a pair of ''Ri.i and fcr-i,i transitions between asymmetric top level pairs which become degenerate at the oblate symmetric top limit. The leading line in the 35C135C1 band consists of overlapped 95t 95* , < transitions, and the value of J decreases by 1 between successive lines down the band. The values of J'' are marked for both bands. The spectrum was acquired using second harmonic detection with 4 khz sinusoidal source modulation and did not require any background subtraction. The sample was at room temperature and pressure of 20 mtorr. high-j na spectrum of chlorobenzene [4], where it was established that the condition for their convergence was planarity of the molecule, the convergence limit being at the oblate symmetric top limit. It was shown that appreciable density of lines in such bands will be observed even for molecules with prolate asymmetry, providing that values of J will be sufficiently large. The relation between rotational constants of a planar molecule is A + B = nc with n = 2 + (3 + x)/v /2 (x + 1), and n was found to be a useful quantity for parameterising the expected convergence of type-ii bands. At the convergence limit n = 4 and its value increases with an increase in prolate character of asymmetry. Diagnostic plots of changes in frequency dispersion of leading lines in type-ii bands as a function of J and of n have been provided in [4]. Subsequently we observed overlapped type-ii na and nb bands for 2-chloroacrylonitrile [8], and the present study reports the first observation of extensive bands of this type for a purely Hb type spectrum. A specimen spectrum is reproduced in Fig. 1, in which je j = 94 band of the common isotopic species is seen to overlap with the j = 96 band of the 37C1 species. Owing to the symmetry equivalence of the two chlorine atoms the intensity the 37C1 isotopomer is 65% of the common species, so that its analysis becomes important for reproducing the whole spectrum. Even though the asymmetry parameter, x for both isotopic species is near 0.6, the J reached in the spectrum in Fig. 1 is sufficient for the essentially oblate type-ii bands to converge to the degree that the first twelve lines fall within 300 MHz. The band lines define only a subset of the constants in the Hamiltonian, so that they were augmented by measurements on the non-band R-type lines such as the two strong lines visible in Fig. 1, and also by Q-type transitions with values of K _ j ranging from 1 to 50. The values of J exceed 90 for both R- and Q-type transitions. Tables of measured frequencies for the common and for the 37C1 species are available from the authors. In the analysis our measurements were

3 349 Z. Kisiel and L. Pszczölkowski Rotational Spectrum of 1,1-Dichloroethylene Table 1. Spectroscopic constants for the ground state of 35C135C1 and 35C137C1 isotopic species of 1,1-dichloroethylene in Watson's Hamiltonian, reduction A. A (MHz) B (MHz) C (MHz) (khz) Ajk (khz) (khz).5, (khz) <5* (khz) *KJ <t>j <t>jk <f>k lines fitted Ofa (MHz) < H,C = C 35C135C1 H2C =C 35CI37CI Ref. [1] This work Ref. [1] This work (15)a (64) (62) (42) (44) (21) (47) (71) (21) (14) (16) (21) (52) (29) (23) (76) (22) (38) (29) (35) (85) (82) (31) (26) (40) (68) (46) a Uncertainties are standard errors in units of the last quoted digit. b Assumed to be the same as in H2C = C 35C135C1. c Deviation of fit per unit weight (27) (12) (13) (39) (18) (24) (17) (34) (74) (41) (30) (14) (47) (11) (61) (11) (20) (15) (65) (83) (98) (18) (10) combined with those from [1], and spectroscopic constants resulting from a fit of Watson's A, Ir Hamiltonian are reported in Table 1. The comparison with previous values shows improvement in accuracy of all constants. In particular, full sets of sextic constants have been determined for the first time for both isotopic species. The data have also been fitted with the S-reduced form of Watson's Hamiltonian, which is sometimes preferred on account of the somewhat smaller intercorrelations between constants, even for molecules which are not very close to the symmetric top limits. For 1,1-dichloroethylene the A- and S-type fits result in identical standard deviations but the latter does indeed confer a slight advantage in intercorrelations. This is evident from the average values of the absolute correlation coefficient, Cy, for the fits, which for the common and the 37C1 species are respectively and for the A-type fit, and and for the S-type fit. The fitted S-reduction constants are reported in Table 2, where they are also compared with the values calculated from the fitted A-type constants by using an inversion of the relations given in [9]. The recalculated values have been assigned errors determined by carrying out error propagation with the aid of a symbolic calculations programme. Since the relations between the A- and S-type constants have been derived with the assumption of a sextic level Hamiltonian, the comparison between the fitted and the calculated constants provides a useful test of whether there are any effective contributions from higher orders to fitted constants. The satisfactory agreement visible in Table 2 shows that this is not the case, although the beginnings of discrepancies may be visible for some constants of the common species, for which there is a larger data set to be fitted. Discussion The spectroscopic constants for 1,1-dichloroethylene determined here should facilitate accurate prediction of the principal features of the rotational spectum of this molecule to considerably higher frequencies than in the present measurements. At high J the contributions to frequencies of the leading lines in type-ii bands reduce to those from only a limited number of constants, in the sequence C, J j, <5j, <Pj5 </>j.... We have, for example, recently observed that for chlorobenzene the frequences of the first ten lines of the j = 175 band

4 350 Z. Kisiel and L. Pszczölkowski Rotational Spectrum of 1,1-Dichloroethylene Table 2. Spectroscopic constants for the common species and the 37C1 isotopomer of 1,1-dichloroethylene in Watson's Hamiltonian, reduction S. The fitted constants are compared with values calculated from the A-reduction constants. H2C = C35C135C1 H2C = C 35C137C1 Fitted Calculated2 Fitted Calculated3 A (MHz) (52) (52) (74) (74) B (MHz) (29) (29) (41) (41) C (MHz) (23) (23) (30) (30) Dj (khz) (70) (79) (95) (147) Djk (khz) (24) (25) (51) (59) Dk (khz) (39) (40) (11) (11) dx (khz) (29) (29) (61) (61) d2 (khz) (10) (10) (29) (30) Hj (63) (94) (11) (23) HJK (37) (116) (70) (236) HKJ (12) (41) (33) (87) Hk (14) (32) (70) (92) hi (37) (40) (89) (99) h (21) (20) (53) (51) hi (57) (58) (12) (12) a Calculated from the A-reduction constants in Table 1. Table 3. Comparison of the quadratic, Ai (uä2), quartic, A (MHz2), and sextic, As (khz2) inertial defects for various molecules. t : AJ(4CAj) J A tc tj) T20, Ref. [10] 0 3, Ref. [11] ONF, Ref. [12] S02, Ref. [13] H2C = CHCN, Ref. [14] C (GHz) (l)a (3) (4) (3) (6) x (5) 12.5 (1) 8.65 (2) 63 (18) x (45)b 578 (111) -70 (12)b 177 (53) i Aq/(4CAj) AJ(6C<Pj) (3) 0.19 (5) HC = CCOOH, Ref. [15] (7) (9) cis-hcic = CFH Ref. [16] (1) -1.6 (3) H2C = CC12, this work (1) (2) H2C = CC1CN, Ref. [8] (1) 2.27 (3) (7) 1.1 (3) c/s-hclc = CC1H, Ref. [17] C (GHz) A (1) (2) (2) (4) (3) 0.31 (3) (1) (3) 0.7 (15) -13 (17) 0.25 (29) 2.3 (7) -0.4 (6) (5) 0.1 (5) (8) -0.2 (2) (1) 0.03 (3) a Errors are standard errors in units of the last quoted digit. b Previous values, 0 3: 4 = 41 (820) khz2, S02: As= -324 (168) khz2, [9], (3) 0.07 (2) (4) (2) (2) (5) at 435 GHz showed a systematic shift of only 50 khz relative to predictions based on data up to j= 104 and 260 GHz. Accurate sextic level constants have recently been determined for several planar molecules, including some comparable in size to 1,1-dichloroethylene. The behaviour of the quadratic planarity defect, has seen much analysis, whereas the properties of the higher quartic Aq, and sextic As, defects are less well known. For reduction-a, representation-f of Watson's Hamiltonian the two higher defects are given by Aq = 4 C A j-(b -C )A JK -2{2A + B + C)öj + 2(B -C )ök, (2)

5 351 Z. Kisiel and L. Pszczölkowski Rotational Spectrum of 1,1-Dichloroethylene As =6C<PJ -(B -C )< P jk-2 (2 A + B + 3C)(t)J + 2(B-Q4>JK, + 4A2J -4 Ö J (4AJ + AJK-2 Ö J -2 Ö K). (3) Watson's analysis for several triatomic molecules [9] showed that while the quartic defect is determinable, the sextic defect is on the verge of being significant. Table 3 reports values of planar defects for 1,1-di chloroethylene, together with values calculated from recently determined A, V Watsonian constants for sev eral molecules. The listing is ordered according to decreasing C, which provides a measure of the in crease in size of the planar molecules. All of these molecules are of appreciable prolate symmetry, with x < 0.5, and the quadratic defect shows a perceptible increasing trend down the table. This can be ratio nalised by an increase in the size of harmonic vibra tion-rotation inertial contributions in larger mole cules, due to the larger number of vibrational modes and a decrease in the frequencies of the lowest fre quency modes. The ordering of molecules in the table is also seen to correspond roughly to decreasing Aq and As. The two higher defects for 1,1-dichloroethylene are somewhat lower than those for the two largest molecules in the table which, in the first approxima tion, may be attributed to the more compact heavy atom arrangement in this molecule. Table 3 shows that Watson's conclusion regarding borderline determinability of As is still valid for the heavier molecules, whereas for the lighter molecules in the first row of the table the level of significance in As is higher and currently near 10% for 0 3. It is of inter est to establish what is the degree of cancellation of terms determining Aq and As, and how these quanti ties scale relative to the size of related spectroscopic constants. It seems natural to use the first terms of (2) [1] R. Wellington Davis and M. C. L. Gerry, J. Mol. Spec trosc. 102, 297 (1983). [2] J. A. Howe and W. H. Flygare, J. Chem. Phys. 36, 440 (1962). [3] J. A. Howe and W. H. Flygare, J. Chem. Phys. 36, 650 (1962). [4] Z. Kisiel, J. Mol. Spectrosc. 144, 381 (1990). [5] Z. Kisiel, J. Mol. Spectrosc. 151, 396 (1992). [6] Z. Kisiel and L. Pszczolkowski, J. Mol. Spectrosc. 158, 318 (1993). [7] S. J. Borchert, J. Mol. Spectrosc. 57, 312 (1975). [8] Z. Kisiel and L. Pszczolkowski, J. Mol. Spectrosc. 166, 32 (1994). [9] J. K. G. Watson, J. Mol. Spectrosc. 65, 123 (1977). [10] F. C. De Lucia, P. Helminger, W. Gordy, H. W. Morgan, and P. A. Staats, Phys. Rev. A8, 2785 (1973). and (3) for such scaling, and for this reason the quan tities AJ{4CAj) and AJ(6C<I>j) are also listed in Table 3. For the heaviest molecules the quartic defect is found to be from one to two hundred times smaller than 4CAj, whereas the ratio involving the sextic defect is smaller as As does not fall much below a tenth of 6 C In summary, Table 3 provides a ready basis for a first estimate of the size of the higher order defects for a wide range of prolate molecules, and for the heaviest molecules currently under study As is expected to be below 1kHz2 and Aq below 0.1 MHz2. The underlying causes for variation in these quantities will, at a more subtle level, differ from molecule to molecule, but the steady decrease in the ratios A J (4 CAj) and AJ(6C<Pj) with molecular size suggests that the applicability of the Hamiltonian increases. In addition to the evaluation of Aq and As it is possible to use relations (2)-(3) and the assumption of zero defect to determine any one of the four centrifu gal distortion constants of a given level from the re maining three. For 1,1,-dichloroethylene the constants evaluated in this way differ from the experimental values by 0.5, 0.3, 3.1, 1.1% for Aj, Sj, AJK, ÖK and 3.0, -1.7,-5.1, 4.0% for <Pj, <\>}, <PJK, (f>jk. The sextic constants for this molecule appear therefore to be very well behaved and can be expected to provide useful additional information on its anharmonic potential [18]. Acknowledgements We are grateful to Prof. G. Cazzoli of University of Bologna for the InSb chip used in the detector. This work was supported from the research grant KBN and the Institute of Physics Research Project No. 6. [11] M. Bellini, P. De Natale, G. Di Lonardo, L. Fusina, M. Inguscio, and M. Prevedelli, J. Mol. Spectrosc. 152, 256 (1992). [12] G. Cazzoli, C. Degli Esposti, P. G. Favero, and P. Palmieri, Nuovo Cim. 3D, 627 (1984). [13] P. A. Helminger and F. C. De Lucia, J. Mol. Spectrosc. Ill, 66 (1985). [14] G. Cazzoli and Z. Kisiel, J. Mol. Spectrosc. 130, 303 (1988). [15] G. Wlodarczak, D. Boucher, J. Burie, and J. Demaison, J. Mol. Spectrosc. 123, 496 (1987). [16] J. L. Alonso, A. G. Lesarri, A. L. Leal, and J. C. Lopez, J. Mol. Spectrosc. 162, 4 (1993). [17] L. A. Leal, J. L. Alonso, and A. G. Lesarri, J. Mol. Spec trosc. 165, 368 (1994). [18] Y. Yamaoka and K. Machida, J. Mol. Spectrosc. 83, 21 (1980).